Solving inequalities is very similar to solving equations with one exception. if we multiply or divide by a negative number, the symbol will need to flip directions. We will keep that in mind as we solve inequalities.

Divide both sides by  

Divide by a negative  flip symbol!  

Graph, starting at , going down with ] for less than or equal to  




Interval Notation 
The inequality we solve can get as complex as the linear equations we solved. We will use all the same patterns to solve these inequalities as we did for solving equations. Just remember that any time we multiply or divide by a negative the symbol switches directions (multiplying or dividing by a positive does not change the symbol!)
Solve and give Interval notation 



Distribute  

Combine like terms  

Move variable to one side  

Subtract 10x from both sides  

Add 20 to both sides  




Divide both sides by 2  




Be careful with graph, x is larger!  




Interval Notation 
Source: Adapted from "Beginning and Intermediate Algebra" by Tyler Wallace, an open source textbook available at: http://wallace.ccfaculty.org/book/book.html